Cardinality and Representation of Stone Relation Algebras

Previous work has axiomatised the cardinality operation in relation algebras, which counts the number of edges of an unweighted graph. We generalise the cardinality axioms to Stone relation algebras, which model weighted graphs, and study the relationships between various axioms for cardinality. This results in simpler cardinality axioms also for relation algebras. We give sufficient conditions for the representability of Stone relation algebras and for Stone relation algebras to be relation algebras.